Nonempirical (double‐hybrid) density functionals applied to atomic excitation energies: A systematic basis set investigation

Abstract

We investigate here the lowest-energy (spin-conserving) excitation energies for the set of He-Ne atoms, with the family of nonempirical PBE, PBE0, PBE0-1/3, PBE0-DH, PBE-CIDH, PBE-QIDH, and PBE0-2 functionals, after employing a wide variety of basis sets systematically approaching the basis set limit: def2-nVP(D), cc-pVnZ, aug-cc-pVnZ, and d-aug-cc-pVnZ. We find that an accuracy (ie, mean unsigned error) of 0.3 to 0.4 eV for time-dependent density functional theory (DFT) atomic excitation energies can be robustly achieved with modern double-hybrid methods, which are also stable with respect to the addition of a double set of diffuse functions, contrarily to hybrid versions, in agreement with recent findings employing sophisticated multiconfigurational DFT methods. K E Y W O R D S atomic excitation energies, diffuse basis functions, double-hybrid density functionals | INTRODUCTIONExcited-state studies continue to be a topic of the most interest, [1][2][3] not only because the underlying theory intrinsically presents challenges for its implementation in common codes but also due to the interplay and large number of factors affecting the final results in molecular and real systems. Whereas ground-state properties still receive much more attention in the ongoing development of density functional theory (DFT) (eg, for built-in datasets and the associated benchmarking of density functional approximations [4,5] ) the applications to atoms are recently emerging as an alternative for the benchmarking of DFT for excited states too. [6][7][8] This is facilitated by the reasonable computational cost of atomic calculations compared to more complex systems, together with the lack of geometry-induced and environmental issues often difficulting the adequate comparison between various theoretical methods.We thus apply here a set of recently developed minimally empirical models, with the time-dependent density functional theory (TD-DFT) formalism, to the lowest-energy and spin-conserving (ΔS = 0) excited-state of atoms from He to Ne. This study aims also at complementing historical studies employing more sophisticated methods, [9][10][11][12][13] as well as shedding light about the performance of some last-generation DFT methods (ie, double-hybrid [DH] functionals) from the fifth rung of the Jacob's ladder. However, dealing with atomic excitation energies unfortunately brings nonnegligible (and severe) basis set issues, due to the presence of valence and Rydberg states, and the challenge they present for an accurate excited-state description in all cases. For instance, it has been recently shown [8] how adding diffuse basis functions to state-of-the-art hybrid functionals dramatically deteriorates the results for standard TD-DFT calculations, with unreasonable errors reaching up to 1.5 to 2.5 eV with respect to experimental values [14] for first-and second-row atoms. Note that the recently developed multiconfigurational pair-density functional theory [15] (MC-PDFT) was instead not affected of such basis set dependence, which clear...

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States

“…In general, we can conclude that the best performances are achieved by the RS DHs, however, the benefit is far from what is expected taking into account the corresponding ground-state tendencies and decreases with increasing the quality of the basis set. Upon closer inspection of the excitation energies of ref ( 126 ), similar findings can be observed for the first- and second-row atoms using nonempirical standard DHs.…”

Assessing challenging intra‐ and inter‐molecular charge‐transfer excitations energies with double‐hybrid density functionals

“…Finally, we have also selected a set of small radicals as examples of electronic transitions in open‐shell molecular systems 52 . Such systems are not routinely studied, and applications of DH methods are still scarce 27 . We do not aim to provide a comprehensive benchmarking of TD‐DFT methods for these systems, but rather we aim to make a first comparison between hybrid and DH functionals (see Tables 6 and 7) in view of the nearly‐exact reference results that have become available recently 52 .…”

“…52 Such systems are not routinely studied, and applications of DH methods are still scarce. 27 We do not aim to provide a comprehensive benchmarking of TD-DFT methods for these systems, but rather we aim to make a first comparison between hybrid and DH functionals (see Tables 6 and 7)…”

“…19 Therefore, for most common TD-DFT applications, the accuracy of excited-state calculations strongly depends on the adequate selection of the underlying exchange-correlation functional, for which comparable benchmark studies beyond those extensively done for ground-state properties are still lacking. Generally speaking, the benchmarking of DH functionals made in recent years, although focused mainly for vertical excitation energies of organic compounds, has nevertheless led to establish that DH models outperform the corresponding hybrid ones for excitation energies [20][21][22][23][24][25][26][27][28] albeit still leaving much room for further improvement. 29,30 Of particular interest is the longstanding goal of improving longrange properties without deteriorating the whole accuracy of the models.…”

Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet–Singlet and Singlet–Triplet Excitation Energies

“…[58][59][60][61][62][63][64] Prior to mid-2020, most of the BLYPbased global DHDFAs studies had been carried out using the full TD-DHDFA scheme, whereas most of the studies using PBE-based global DHDFAs had used the TDA-DHDFA scheme, instead. 37,38,[65][66][67][68][69][70][71][72][73][74][75] Moreover, all previous benchmark studies and applications had been limited to singlet-singlet excitations, except for the original work by Grimme and Neese from 2007, 18 leaving out other spin multiplicities of crucial relevance, such as triplet excitations, most likely due to the lack of a code that could handle those transitions. For this reason, we assessed for the first time singlet-singlet and singlet-triplet excitations with global-and LC-DHDFAs based on both BLYP and PBE expressions for the underlying exchange-correlation functional and compared them with hybrid functionals.…”